A two-wheeled self-balancing robot is considered for investigating the responses of a control moment gyroscope powered by a proportional controller to prevent the robot rollover against the constant inertia forces because of accelerations of the wheels of the robot. The amplitudes of the frequency equations related to the required angular momentum of flywheels with an optimum controller gain were also found. A simulation model of the robot using computer-aided engineering software (RecurDyn) is built to verify the equations of a Lagrangian model. The results of both obtained from the Lagrangian and that from RecurDyn simulations are analyzed comparatively, in which the proportional control loop reduces the required flywheel speeds Ω of gyros and keeps the robot in a very small amplitude of a stable sinusoidal motion in the upright position.
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